```Quiz 3 Ch 5
If r+si is a solution to the equation ax2+bx +4 =y with s not = 0, express the coordinates of the vertex of
the parabola in terms of r and s. Show all steps.
Quiz 3 Ch 5
If r+si is a solution to the equation ax2+bx +4 =y with s not = 0, express the coordinates of the vertex of
the parabola in terms of r and s. Show all steps.
Solution
We know from the quadratic formula that r+si =
Separating into real and imaginary parts
or if you factor out i  =
=
−+√2 −4
2
−
2
and  =
−
2
=
2
√−2 +4
2
Looking at the quadratic equation in vertex form  −
ℎ=
√2 −4
−2 +4
4
−2 +4
=  ( +

2
2
)
4
Since r is h, the x coordinate of the vertex is  =
−
2
Comparing s and k, the y coordinate of the vertex yields  =
√−2 +4
2
−2 +4
4
With some algebra  2 =
−2 +4
42
k=
so k= 2
Then the coordinates of the vertex in terms of r and s are (,  2 )
Solution
We know from the quadratic formula that r+si =
Separating into real and imaginary parts
or if you factor out i  =
=
−+√2 −4
−
2
2
and  =
ℎ=
2
=
2
√−2 +4
2
Looking at the quadratic equation in vertex form  −
−
√2 −4
−2 +4
−2 +4
4
=  ( +

2
)
2
4
Since r is h, the x coordinate of the vertex is  =
−
2
Comparing s and k, the y coordinate of the vertex yields  =
−2 +4
4
With some algebra  2 =
−2 +4
42
√−2 +4
2
so k= 2
Then the coordinates of the vertex in terms of r and s are (,  2 )
k=
```